By Rosario Gennaro, Matthew Robshaw
The volume-set, LNCS 9215 and LNCS 9216, constitutes the refereed lawsuits of the thirty fifth Annual foreign Cryptology convention, CRYPTO 2015, held in Santa Barbara, CA, united states, in August 2015. The seventy four revised complete papers provided have been conscientiously reviewed and chosen from 266 submissions. The papers are geared up within the following topical sections: lattice-based cryptography; cryptanalytic insights; modes and buildings; multilinear maps and IO; pseudorandomness; block cipher cryptanalysis; integrity; assumptions; hash capabilities and circulation cipher cryptanalysis; implementations; multiparty computation; zero-knowledge; idea; signatures; non-signaling and information-theoretic crypto; attribute-based encryption; new primitives; and completely homomorphic/functional encryption.
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Extra resources for Advances in Cryptology -- CRYPTO 2015: 35th Annual Cryptology Conference, Santa Barbara, CA, USA, August 16-20, 2015, Proceedings, Part I
17] for LWE or Albrecht et al.  for binary-LWE) and the estimates (under certain models [11,25,26,29]) for distinguishing LWE (or binary-LWE) samples from uniform using lattice reduction algorithms, when LWE is reduced to SIS. The results consolidate the understanding that BKW is asymptotically eﬃcient. For the toy LWE instances with n = 128, the SIS approach still beats all the BKW variants, including ours; but the recent variant has greatly narrowed the gap. The situation alters when the parameter n increases.
Proof. If all reduced angles are 90◦ , then we can simply let θ1 = π3 and θ2 = π2 and use the hash family described in Sect. 5 with p1 = 23 and p2 = 12 . 585. 3289n+o(n) ˜ )=2 . 3366n+o(n) Of course, in practice not all reduced angles are actually 90◦ , and one should carefully analyze what is the real probability that a vector w whose angle with v is more than 60◦ , is found as a candidate due to a collision in one of the hash tables. The following central theorem follows from this analysis and shows how to choose the parameters to optimize the asymptotic time complexity.
SVP challenge (2014). org/svp-challenge 43. : A hierarchy of polynomial time lattice basis reduction algorithms. Theoret. Comput. Sci. 53(2), 201–224 (1987) 44. : Lattice basis reduction: improved practical algorithms and solving subset sum problems. Math. Programming 66(2), 181–199 (1994) 45. : Improved Nguyen-Vidick heuristic sieve algorithm for shortest vector problem. In: ASIACCS, pp. 1–9 (2011) 46. : A three-level sieve algorithm for the shortest vector problem. , Lisonˇek, P. ) SAC 2013.
Advances in Cryptology -- CRYPTO 2015: 35th Annual Cryptology Conference, Santa Barbara, CA, USA, August 16-20, 2015, Proceedings, Part I by Rosario Gennaro, Matthew Robshaw